#!/usr/bin/env python
"""Simple data fitting and smoothing example"""
XXX = None # placeholder for missing pieces
from numpy import exp,arange,array,linspace
from numpy.random import normal
from scipy.optimize import leastsq
from scipy.interpolate import splrep,splev
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
def func(pars):
a, alpha, k = pars
return a*exp(alpha*x_vals) + k
def errfunc(pars):
"""Return the error between the function func() evaluated"""
return y_noisy - func(pars) #return the error
# Use globals for the x values and true parameters
pars_true = array([2.0, -.76, 0.1])
x_vals = linspace(0, 4, 1000)
# some pseudo data; add some noise
y_noisy = func(pars_true) + normal(0.0, 0.1, x_vals.shape)
# the intial guess of the params
guess = 1.0, -.4, 0.0
# now solve for the best fit paramters
#XXX - use leastsq() here, call the output 'best' for code below to use
best = XXX
print 'Least-squares fit to the data'
print 'true', pars_true
print 'best', best
print '|err|_l2 =',np.linalg.norm(pars_true-best)
# scipy's splrep uses FITPACK's curfit (B-spline interpolation)
print
print 'Spline smoothing of the data'
sp = XXX # use splrep()
smooth = XXX # use splev()
print 'Spline information (see splrep and splev for details):',sp
# Polynomial fitting
def plot_polyfit(x,y,n,fignum=None):
"""Do a polynomial fit of order n and plot it."""
if fignum is None:
fignum = plt.figure().number
plt.plot(x,y,label='Data')
fit_coefs = XXX # use np.polyfit here
fit_val = XXX # use np.polyval
plt.plot(x,fit_val,label='Polynomial fit, $n=%d$' % n)
plt.legend()
return fignum
# Now use pylab to plot
plt.figure()
# Plot the least-squares fit here...
plt.plot(x_vals,y_noisy,label='Noisy data')
plt.plot(x_vals,func(best),lw=2,label='Least-squares fit')
plt.legend()
plt.figure()
# Plot the splines fit here...
# Plot the polynomials fits with this:
fignum = plot_polyfit(x_vals,y_noisy,1)
plot_polyfit(x_vals,y_noisy,2,fignum)
plot_polyfit(x_vals,y_noisy,3,fignum)
plt.show()
